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Penelope states the unsub lost his fingers in a buzz saw accident when he was 12. The record she is reading shows his date of birth as Jan. 18, 1962. The medical record shows the accident was in 1999, so the unsub would have been 37, not 12, and it was a sabre saw, not a buzz saw, which are quite different.
The Navy would have jurisdiction if a Marine were killed, and would head the investigation, not the FBI.
When the unsub hangs the third victim, as with all the victims, he kicks the chair from right under his feet. When the team drives up to the hanging body, it hangs a lot higher than it should.
The fighting style Cooper is practicing at the beginning and end of the episode is Kali, a Filipino martial art that specializes in using sticks and short- to medium-length blades as extensions of the body.
When SSA Griffith finds the obit, she tells SSA Rawson that the man died in Hope Memorial following surgery. She then reports to Cooper that she found an obit for a man who died following surgery, and he adds that their victim's surgery was also scheduled for Hope Memorial. As they leave, Cooper says, "One man dies after knee surgery and another one dies before it." Up to that point, there was no mention of what type of surgery was performed on the man in the hospital.